Answer :
To simplify the fraction [tex]\(\frac{11}{21}\)[/tex], you need to find the greatest common divisor (GCD) of the numerator and the denominator.
Here are the steps:
1. Identify the numerator and denominator:
- The numerator is 11.
- The denominator is 21.
2. Find the GCD of 11 and 21:
- The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- Upon examining 11 and 21, we see that 11 is a prime number, and it doesn't divide 21.
- Therefore, the GCD of 11 and 21 is 1.
3. Simplify the fraction:
- To simplify the fraction, divide both the numerator and the denominator by their GCD.
- Thus, we divide 11 by 1 and 21 by 1.
[tex]\[ \frac{11 \div 1}{21 \div 1} = \frac{11}{21} \][/tex]
4. Conclusion:
- The fraction [tex]\(\frac{11}{21}\)[/tex] is already in its simplest form because the numerator and the denominator have no common factors other than 1.
Hence, the simplified form of the fraction [tex]\(\frac{11}{21}\)[/tex] is [tex]\(\frac{11}{21}\)[/tex], and the GCD of 11 and 21 is 1.
Here are the steps:
1. Identify the numerator and denominator:
- The numerator is 11.
- The denominator is 21.
2. Find the GCD of 11 and 21:
- The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- Upon examining 11 and 21, we see that 11 is a prime number, and it doesn't divide 21.
- Therefore, the GCD of 11 and 21 is 1.
3. Simplify the fraction:
- To simplify the fraction, divide both the numerator and the denominator by their GCD.
- Thus, we divide 11 by 1 and 21 by 1.
[tex]\[ \frac{11 \div 1}{21 \div 1} = \frac{11}{21} \][/tex]
4. Conclusion:
- The fraction [tex]\(\frac{11}{21}\)[/tex] is already in its simplest form because the numerator and the denominator have no common factors other than 1.
Hence, the simplified form of the fraction [tex]\(\frac{11}{21}\)[/tex] is [tex]\(\frac{11}{21}\)[/tex], and the GCD of 11 and 21 is 1.
